Aman can swim with a speed of 5m / s in calm water . if this man swims across a specific river his speed is 3m / s . if he takes the minimum time to cross the river find the speed of the flow of water in the river .
. plz answer me with all the steps !

4 m/s

Explanation:

It doesn't state it clearly in the problem, but I assume that the shores of the river are parallel and the man reaches the other side perpendicular from where he started (see attached image).

There are an infinite number of ways the swimmer can go from point A to point B, but the shortest time is of course a straight line.  We know that the net speed along this line is 3 m/s.  We also know the swimmer's speed is 5 m/s.  Since the net velocity vector is perpendicular to the river's velocity, we can use Pythagorean theorem.

vᵣ² + (3 m/s)² = (5 m/s)²

vᵣ = 4 m/s

The water in the river flows at a speed of 4 m/s.

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